The basic reproduction number, R0R_0, in structured populations

In this paper, we provide a straightforward approach to defining and deriving the key epidemiological quantity, the basic reproduction number, $R_0$, for Markovian epidemics in structured populations. The methodology derived is applicable to, and demonstrated on, both $SIR$ and $SIS$ epidemics and allows for population as well as epidemic dynamics. The approach taken is to consider the epidemic process as a multitype process by identifying and classifying the different types of infectious units along with the infections from, and the transitions between, infectious units. For the household model, we show that our expression for $R_0$ agrees with earlier work despite the alternative nature of the construction of the mean reproductive matrix, and hence, the basic reproduction number.Comment: 26 page

Network modelling for sexually transmitted diseases

The aim of this thesis is to propose suitable mathematical models for the analysis of sexually transmitted disease epidemics. We are interested in a closed population, where infections are only transmitted through heterosexual contacts. The population is hence divided into two groups: male and female. Individuals are classified according to gender, relationship and disease status. Both stochastic and deterministic SIS models are employed. The stochastic models are formulated in terms of a Markov process with a finite state space. Two main models are constructed and quantities of interest such as the basic reproduction number and endemic level of the sexually transmitted disease (STD) are obtained. The first model is formulated to describe dynamics of STDs, where the sexual behaviour is considered “faithful”. By being faithful, we mean individuals are monogamous, and there are no casual sexual contacts (one-night stands). The early stages of the epidemic are approximated by a 2-type branching process. This allows us to compute the following quantities of interest, the threshold parameter (R0) and the probability of extinction. In order to study the endemic level, it is helpful to use the deterministic (ODE) approximation of the stochastic SIS epidemic. The behaviour about the endemic equilibrium is studied using an Ornstein-Uhlenbeck process. Stochastic simulations are utilised to obtain the mean time to extinction. The second model is an extension of the first model, where casual sexual contacts (one - night stands) are included in the model. The model is again a Markov process but its analysis is more involved. A key difference is now a 5 type branching process is used to approximate the initial stages of the epidemic, to determine the threshold parameter (R0) and the probability of extinction. Other quantities of interest are studied through similar approaches. Medication use is studied as a control measure in this thesis. We introduce a new parameter (v) governing the medication use into both models. Throughout we study the effect of the control strategies on the key quantities of interest highlighted above

The basic reproduction number, R_0, in structured populations

In this paper, we provide a straightforward approach to defining and deriving the key epidemiological quantity, the basic reproduction number, $R_0$, for Markovian epidemics in structured populations. The methodology derived is applicable to, and demonstrated on, both $SIR$ and $SIS$ epidemics and allows for population as well as epidemic dynamics. The approach taken is to consider the epidemic process as a multitype process by identifying and classifying the different types of infectious units along with the infections from, and the transitions between, infectious units. For the household model, we show that our expression for $R_0$ agrees with earlier work despite the alternative nature of the construction of the mean reproductive matrix, and hence, the basic reproduction number

Narrow-Band Light-Emitting Diodes (LEDs) Effects on Sunflower (Helianthus annuus) Sprouts with Remote Monitoring and Recording by Internet of Things Device

Previous studies have demonstrated that light quality critically affects plant development and growth; however, the response depends upon the plant species. This research aims to examine the effects of different light wavelengths on sunflower (Helianthus annuus) sprouts that were stimulated during the night. Natural light and narrow-band light-emitting diodes (LEDs) were used for an analysis of sunflower sprouts grown under full light and specific light wavelengths. Sunflower seeds were germinated under different light spectra including red, blue, white, and natural light. Luminosity, temperature, and humidity sensors were installed in the plant nursery and remotely monitored and recorded by an Internet of Things (IoT) device. The experiment examined seed germination for seven days. The results showed that the red light had the most influence on sunflower seed germination, while the natural light had the most influence on the increase in the root and hypocotyl lengths